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{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFind a pair of positive integers $(x, y)$ that satisfies the equation $3... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nCalculate the area of a triangle with vertices at $(0,0)$, $(9, 0)$, and... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nLet $S = \\sum_{k \\equiv 0 \\pmod{3}} \\binom{14}{k}$. Find the value o... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA factory has 1000 widgets. Each step: 12% are lost to defects (floor), ... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA point is chosen at random on a line segment of length 13. What is the ... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFind the remainder when $5^{114}$ is divided by $7$."
},
{
"role... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFind a pair of positive integers $(x, y)$ that satisfies the equation $1... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA budget of 1000 dinars is allocated: Salaries gets 40%, Equipment gets ... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nAmira and Rashid must split 149 points as fairly as possible. The first ... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA company earned 8595 dollars. A 18% tax is applied (floor). How much ta... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nCalculate the area of a triangle with vertices at $(0,0)$, $(8, 0)$, and... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA point is chosen at random on a line segment of length 12. What is the ... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nIn $\\triangle ABC$, side $a = 8$, side $b = 4$, and $\\angle C = 60^\\c... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA sequence is defined by $a_0 = 2$, $a_1 = 1$, and $a_n = 2a_{n-1} + 1a_... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA sequence is defined by $a_0 = 2$, $a_1 = 2$, and $a_n = 1a_{n-1} + 1a_... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFour players have scores: Sam=35, Kim=62, Dan=100, Eve=32. The lowest sc... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nThree merchants — Hassan, Leila, and Waleed — have 64, 37, and 29 apples... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA convex quadrilateral has vertices at $(0, 0)$, $(5, 0)$, $(7, 9)$, and... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA sequence is defined by $a_0 = 0$, $a_1 = 1$, $a_2 = 1$, and $a_n = a_{... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nLet $\\omega = e^{2\\pi i / 4}$. Find the value of the product $\\prod_{... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nCalculate the area of a triangle with vertices at $(0,0)$, $(6, 0)$, and... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nIn $\\triangle ABC$, $AC = 5$ and $AB = 5$. A cevian $AD$ is drawn to si... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFind a pair of positive integers $(x, y)$ that satisfies the equation $1... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA merchant sold goods worth 4983 gold coins. A 25% tax is applied (floor... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFind the smallest positive integer $x$ such that:\n$x \\equiv 2 \\pmod{5... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA function $f(x)$ satisfies $f(x+y) = f(x) + f(y)$ for all $x, y$. If $f... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nIn $\\triangle ABC$, side $a = 4$, side $b = 6$, and $\\angle C = 60^\\c... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA budget of 5000 dollars is allocated: Salaries gets 40%, Equipment gets... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nCompute $4^{393} \\pmod{15}$."
},
{
"role": "assistant",
"co... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nIn $\\triangle ABC$, $AC = 5$ and $AB = 5$. A cevian $AD$ is drawn to si... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA stockpile of 3201 items grows by 5% each step (floor). What is the amo... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nEvaluate the finite sum: $\\sum_{n=1}^{5} \\frac{1}{n(n+2)}$."
},
{
... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nHow many ways are there to distribute 12 identical gold coins among 4 di... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA company earned 1466 dollars. A 5% tax is applied (floor). How much tax... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nIf $x + y = 6$ and $xy = 2$, find the value of $x^3 + y^3$."
},
{
... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFind the value of $(1 + i)^{6}$, where $i$ is the imaginary unit ($i^2 =... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFind a pair of positive integers $(x, y)$ that satisfies the equation $1... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nCompute $4^{418} \\pmod{15}$."
},
{
"role": "assistant",
"co... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFour players have scores: Aya=20, Kai=87, Nia=64, Rex=26. The lowest sco... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFour players have scores: Aya=96, Kai=77, Nia=29, Rex=86. The lowest sco... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nIn $\\triangle ABC$, $AC = 5$ and $AB = 5$. A cevian $AD$ is drawn to si... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nAya, Kai, Nia, Rex must split 301 points proportional to their contribut... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nEvaluate the finite sum: $\\sum_{n=1}^{5} \\frac{1}{n(n+1)}$."
},
{
... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nIn $\\triangle ABC$, $AC = 5$ and $AB = 5$. A cevian $AD$ is drawn to si... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA main office has 269 barrels of oil. Day 1: Ships 25% (floor) to Satell... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nAmira and Rashid start with 84 and 90 stamps. Each round, the one with m... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFind a pair of positive integers $(x, y)$ that satisfies the equation $8... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA point is chosen at random on a line segment of length 14. What is the ... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nLet $S = \\sum_{k \\equiv 0 \\pmod{4}} \\binom{16}{k}$. Find the value o... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nMia, Leo, Zoe, Jay must split 242 stamps proportional to their contribut... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nAn investment of 2722 dollars shrinks by 15% each step (floor). What is ... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nHow many ways are there to distribute 9 identical gold coins among 4 dis... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nThree accounts (Ali, Babak, Cyrus) hold 374, 449, and 266 gold coins (to... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nContestants have scores: Hassan=57, Leila=65, Waleed=62. Step 1: The low... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nGame show: Mona=85, Faris=112, Salma=112 coins. Round 1: Each wagers 30%... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA function $f(x)$ satisfies $f(x+y) = f(x) + f(y)$ for all $x, y$. If $f... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nIn a class of 100 students, 52 like Math and 51 like Science. If 37 stud... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA sequence is defined by $a_0 = 0$, $a_1 = 3$, and $a_n = 3a_{n-1} + 2a_... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nCalculate the area of a triangle with vertices at $(0,0)$, $(7, 0)$, and... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nLet $p = 5$. Let $a = 46$ and $b = 21$. Find the largest power of $5$ th... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA convex quadrilateral has vertices at $(0, 0)$, $(6, 0)$, $(8, 10)$, an... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nAli and Babak must split 63 bags of rice as fairly as possible. The olde... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA farmer harvested crops worth 6882 silver. A 5% tax is applied (floor).... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA system starts with 271 units. Each step: 10% is removed (floor), then ... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFind the number of non-negative integer solutions to $x_1 + x_2 + x_3 = ... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nLet $\\omega = e^{2\\pi i / 5}$. Find the value of the product $\\prod_{... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA point is chosen at random on a line segment of length 19. What is the ... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA convex quadrilateral has vertices at $(0, 0)$, $(6, 0)$, $(6, 9)$, and... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFind the remainder when $12^{958}$ is divided by $13$."
},
{
"ro... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA group of 3 friends must divide 95 points equally. Each gets the floor ... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA function $f(x)$ satisfies $f(x+y) = f(x) + f(y)$ for all $x, y$. If $f... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA warehouse has 880 diamonds. Day 1: Ships 30% (floor) to Store A and 15... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA function $f(x)$ satisfies $f(x+y) = f(x) + f(y)$ for all $x, y$. If $f... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA water tank has 200 liters. Each step: 10% evaporates (floor), then 37 ... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nIn $\\triangle ABC$, $AC = 5$ and $AB = 5$. A cevian $AD$ is drawn to si... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nLet $\\omega = e^{2\\pi i / 5}$. Find the value of the product $\\prod_{... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA sequence is defined by $a_0 = 2$, $a_1 = 3$, and $a_n = 3a_{n-1} + 1a_... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nHow many ways are there to distribute 9 identical gold coins among 3 dis... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA group of 6 friends must divide 979 apples equally. Each gets the floor... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nCompute $4^{280} \\pmod{21}$."
},
{
"role": "assistant",
"co... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nIn a class of 100 students, 47 like Math and 45 like Science. If 31 stud... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA stockpile has 800 supplies. Each step: 20% are used up (floor), then 2... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nEvaluate the finite sum: $\\sum_{n=1}^{5} \\frac{1}{n(n+1)}$."
},
{
... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA sequence is defined by $a_0 = 1$, $a_1 = 3$, and $a_n = 1a_{n-1} + 1a_... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA convex quadrilateral has vertices at $(0, 0)$, $(5, 0)$, $(5, 8)$, and... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA merchant sold goods worth 7995 gold coins. A 20% tax is applied (floor... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nHow many ways are there to distribute 6 identical gold coins among 4 dis... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA function $f(x)$ satisfies $f(x+y) = f(x) + f(y)$ for all $x, y$. If $f... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nThree merchants — Khalid, Fatima, and Jaber — have 48, 28, and 15 stamps... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFour players have scores: Ada=73, Ben=78, Cal=95, Dee=44. The lowest sco... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nLayla, Omar, Rania must split 152 bags of rice proportional to their con... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nEvaluate the finite sum: $\\sum_{n=1}^{5} \\frac{1}{n(n+1)}$."
},
{
... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA point is chosen at random on a line segment of length 16. What is the ... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFour players have scores: Aya=51, Kai=25, Nia=52, Rex=82. The lowest sco... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA sequence is defined by $a_0 = 2$, $a_1 = 2$, and $a_n = 3a_{n-1} + 2a_... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nAn investment of 1877 dollars grows by 12% each step (floor). What is th... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFrom an external point $P$, a tangent $PT$ and a secant $PAB$ are drawn ... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA group of 9 team members must divide 889 gold coins equally. Each gets ... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nCompute $4^{107} \\pmod{21}$."
},
{
"role": "assistant",
"co... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFind a pair of positive integers $(x, y)$ that satisfies the equation $1... |
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Check out the documentation for more information.
🔱 AIME-God v5.2 "Zero-System" (Training)
The ultimate dataset for fine-tuning models to master the AIME/Olympiad math competitions, specifically targeting the hardest Tier-15 (problems 11-15).
🚀 Key Features
- Zero-System Strategy: System instructions are merged into the first User turn for 100% compatibility with Vertex AI Induction and Managed SFT.
- Tier-15 Mastery: Includes high-density examples for LTE Lemma, Geometric Inversion, Barycentric Coordinates, Generating Functions, and Roots of Unity Filters.
- Reasoning Depth: 50,000 rows of pure, high-signal reasoning blocks with explicit
<think>steps.
📊 Dataset Structure
- Format: Conversational JSONL (
messageslist) - Roles:
user,assistant(System prompt merged into first user message). - Target: Qwen-3-8B / Llama-3-8B fine-tuning.
⚙️ Recommended Training Config
- Epochs: 2
- Adapter: LoRA (Rank 16)
- Learning Rate: 1e-5
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